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Volumn 52, Issue 10, 2006, Pages 4581-4594

Maiorana-McFarland class: Degree optimization and algebraic properties

Author keywords

Algebraic degree; Algebraic immunity; Boolean function; Nonlinearity; Rectorial Boolean function; Resiliency

Indexed keywords

CRYPTOGRAPHY; NONLINEAR FILTERING; NONLINEAR SYSTEMS; OPTIMIZATION;

EID: 33947416944     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.881721     Document Type: Article
Times cited : (25)

References (39)
  • 1
    • 85002229923 scopus 로고
    • On correlation-immune functions
    • Advances in Cryptology, EUROCRYPT'91 , Berlin, Germany: Springer-Verlag
    • P. Camion, C. Carlet, P. Charpin, and N. Sendrier, "On correlation-immune functions," in Advances in Cryptology - EUROCRYPT'91 (Lecture Notes in Computer Sceince). Berlin, Germany: Springer-Verlag, 1991, vol. 547, pp. 86-100.
    • (1991) Lecture Notes in Computer Sceince , vol.547 , pp. 86-100
    • Camion, P.1    Carlet, C.2    Charpin, P.3    Sendrier, N.4
  • 2
    • 0009963317 scopus 로고    scopus 로고
    • On the coset weight divisibility and nonlinearity of resilient and correlation-immune functions
    • New York: Springer-Verlag
    • C. Carlet, "On the coset weight divisibility and nonlinearity of resilient and correlation-immune functions," in Special Issue of Discr. Math. Theor. Comp. Sci., New York: Springer-Verlag, 2001, pp. 131-144.
    • (2001) Special Issue of Discr. Math. Theor. Comp. Sci , pp. 131-144
    • Carlet, C.1
  • 3
    • 84937394144 scopus 로고    scopus 로고
    • A larger class of cryptographic Boolean functions via a study of the Maiorana-Mcfarland constructions
    • Advances in Cryptology, CRYPTO, Berlin, Germany: Springer-Verlag
    • _, "A larger class of cryptographic Boolean functions via a study of the Maiorana-Mcfarland constructions," in Advances in Cryptology - CRYPTO 2002 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 2002, vol. 2442, pp. 549-564.
    • (2002) Lecture Notes in Computer Science , vol.2442 , pp. 549-564
    • Carlet, C.1
  • 4
    • 0036160819 scopus 로고    scopus 로고
    • Spectral domain analysis of correlation immune and resilient Boolean functions
    • C. Carlet and P. Sarkar, "Spectral domain analysis of correlation immune and resilient Boolean functions," Finite Fields Their Applic., vol. 8, no. 1, pp. 120-130, 2002.
    • (2002) Finite Fields Their Applic , vol.8 , Issue.1 , pp. 120-130
    • Carlet, C.1    Sarkar, P.2
  • 5
    • 24944507616 scopus 로고    scopus 로고
    • Highly nonlinear resilient functions through disjoint codes in projective spaces
    • P. Charpin and E. Pasalic, "Highly nonlinear resilient functions through disjoint codes in projective spaces," Des., Codes, Cryptogr., vol. 37, no. 2, pp. 319-346, 2005.
    • (2005) Des., Codes, Cryptogr , vol.37 , Issue.2 , pp. 319-346
    • Charpin, P.1    Pasalic, E.2
  • 6
    • 84955576233 scopus 로고    scopus 로고
    • On the correlation immune functions and their nonlinearity
    • Advances in Cryptology, ASI-ACRYPT'96 , Berlin, Germany: Springer-Verlag
    • S. Chee, S. Lee, D. Lee, and H. S. Sung, "On the correlation immune functions and their nonlinearity," in Advances in Cryptology - ASI-ACRYPT'96 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 1996, vol. 1163, pp. 232-243.
    • (1996) Lecture Notes in Computer Science , vol.1163 , pp. 232-243
    • Chee, S.1    Lee, S.2    Lee, D.3    Sung, H.S.4
  • 7
    • 84880887203 scopus 로고    scopus 로고
    • Nonlinear vector resilient functions
    • Advances in Cryptology, CRYPTO, Berlin, Germany: Springer-Verlag
    • J. H. Cheon, "Nonlinear vector resilient functions," in Advances in Cryptology - CRYPTO 2001 (Lecture Notes in Computer Sceince). Berlin, Germany: Springer-Verlag, 2001, vol. 2139, pp. 181-195.
    • (2001) Lecture Notes in Computer Sceince , vol.2139 , pp. 181-195
    • Cheon, J.H.1
  • 8
    • 35248828626 scopus 로고    scopus 로고
    • Higher order correlation attacks, XL algorithm and cryptoanalysis of Toyocrypt
    • Berlin, Germany: Springer-Verlag
    • N. Courtois, "Higher order correlation attacks, XL algorithm and cryptoanalysis of Toyocrypt," in P roc. ICISC 2002 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 2002, vol. 2587, pp. 182-199.
    • (2002) P roc. ICISC 2002 (Lecture Notes in Computer Science) , vol.2587 , pp. 182-199
    • Courtois, N.1
  • 9
    • 33746353310 scopus 로고    scopus 로고
    • Algebraic attacks on combiner with memory and several outputs
    • Proc. ISICS 2004 , Berlin, Germany: Springer-Verlag
    • _, "Algebraic attacks on combiner with memory and several outputs," in Proc. ISICS 2004 (Lecture Notes in Computer Sceince). Berlin, Germany: Springer-Verlag, 2004.
    • (2004) Lecture Notes in Computer Sceince
    • Courtois, N.1
  • 10
    • 21144436473 scopus 로고    scopus 로고
    • Algebraic attacks on stream ciphers with linear feedback
    • Berlin, Germany: Springer-Verlag
    • N. Courtois and W. Meier, "Algebraic attacks on stream ciphers with linear feedback," in Advances in Cryptology - EUROCRYPT 2003. Berlin, Germany: Springer-Verlag, 2003, vol. 2656, pp. 346-359.
    • (2003) Advances in Cryptology - EUROCRYPT 2003 , vol.2656 , pp. 346-359
    • Courtois, N.1    Meier, W.2
  • 11
    • 35048830936 scopus 로고    scopus 로고
    • Algebraic Immunity for Cryptographically Significant Boolean Functions
    • Berlin, Germany: Springer-Verlag
    • D. K. Dalai, K. C. Gupta, and S. Maitra, Algebraic Immunity for Cryptographically Significant Boolean Functions (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 2004, vol. 3348, pp. 92-106.
    • (2004) Lecture Notes in Computer Science , vol.3348 , pp. 92-106
    • Dalai, D.K.1    Gupta, K.C.2    Maitra, S.3
  • 12
    • 26444607970 scopus 로고    scopus 로고
    • Cryptographically significant Boolean functions: Construction and analysis in terms of algebraic immunity
    • Fast Software Encryption, Berlin, Germany: Springer-Verlag
    • _, "Cryptographically significant Boolean functions: Construction and analysis in terms of algebraic immunity," in Fast Software Encryption 2005 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 2005, vol. 3557, pp. 98-111.
    • (2005) Lecture Notes in Computer Science , vol.3557 , pp. 98-111
    • Dalai, D.K.1    Gupta, K.C.2    Maitra, S.3
  • 13
    • 0003797192 scopus 로고
    • Elementary Haddamard Difference Sets,
    • Ph.D. dissertation. Univ.Maryland, College Park, MD
    • J. F. Dillon, "Elementary Haddamard Difference Sets," Ph.D. dissertation. Univ.Maryland, College Park, MD, 1974.
    • (1974)
    • Dillon, J.F.1
  • 14
    • 84948983734 scopus 로고
    • Construction of bent functions and balanced Boolean functions with high nonlinearity
    • Fast Sofnrare Encryption, Cambridge Security Workshop , Berlin, Germany: Springer-Verlag
    • H. Dobbertin, "Construction of bent functions and balanced Boolean functions with high nonlinearity," in Fast Sofnrare Encryption, Cambridge Security Workshop (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 1994, vol. 1008, pp. 61-74.
    • (1994) Lecture Notes in Computer Science , vol.1008 , pp. 61-74
    • Dobbertin, H.1
  • 15
    • 84958755583 scopus 로고    scopus 로고
    • Improved constructions of nonlinear resilient S-boxes
    • Advances in Cryptology, ASIACRYPT, Berlin, Germany: Springer-Verlag
    • K. C. Gupta and P. Sarkar, "Improved constructions of nonlinear resilient S-boxes," in Advances in Cryptology - ASIACRYPT 2002 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 2002, vol. 2501, pp. 466-483.
    • (2002) Lecture Notes in Computer Science , vol.2501 , pp. 466-483
    • Gupta, K.C.1    Sarkar, P.2
  • 16
    • 84957062097 scopus 로고    scopus 로고
    • Fast correlation attacks based on turbo code techniques
    • Advances in Cryptology, CRYPTO'99 , Berlin, Germany: Springer-Verlag
    • T. Johansson and F. Jönsson, "Fast correlation attacks based on turbo code techniques," in Advances in Cryptology - CRYPTO'99 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 1999, vol. 1666, pp. 181-197.
    • (1999) Lecture Notes in Computer Science , vol.1666 , pp. 181-197
    • Johansson, T.1    Jönsson, F.2
  • 17
    • 84957702423 scopus 로고    scopus 로고
    • Improved fast correlation attacks on stream ciphers via convolutional codes
    • Advances in Cryptology, EUROCRYPT'99 , Berlin, Germany: Springer-Verlas
    • _, "Improved fast correlation attacks on stream ciphers via convolutional codes," in Advances in Cryptology - EUROCRYPT'99 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlas, 1999, vol. 1592, pp. 347-362.
    • (1999) Lecture Notes in Computer Science , vol.1592 , pp. 347-362
    • Johansson, T.1    Jönsson, F.2
  • 18
    • 0037319586 scopus 로고    scopus 로고
    • A construction of resilient functions with high nonlinearity
    • Feb
    • T. Johansson and E. Pasalic, "A construction of resilient functions with high nonlinearity," IEEE Trans. Inf. Theory, vol. 49, no. 2, pp. 494-501, Feb. 2003.
    • (2003) IEEE Trans. Inf. Theory , vol.49 , Issue.2 , pp. 494-501
    • Johansson, T.1    Pasalic, E.2
  • 19
    • 33947408509 scopus 로고    scopus 로고
    • L. R. Knudsen, Quadratic Relations in Khazad and Whirlpool, Rep.: New European Schemes for Signatures, Integrity and Encryption, NES/DOC/UIB/WP5/017/1 [Online]. Available: http://www.cosic.esat.kuleuven.be/nessie/reports/
    • L. R. Knudsen, Quadratic Relations in Khazad and Whirlpool, Rep.: New European Schemes for Signatures, Integrity and Encryption, NES/DOC/UIB/WP5/017/1 [Online]. Available: http://www.cosic.esat.kuleuven.be/nessie/reports/
  • 20
    • 0001689688 scopus 로고    scopus 로고
    • Highly nonlinear f-resilient functions
    • K. Kurosawa, T. Satoh, and K. Yamamoto, "Highly nonlinear f-resilient functions," J. Univ. Comp. Sci., vol.3, no. 6, pp.721-729, 1997.
    • (1997) J. Univ. Comp. Sci , vol.3 , Issue.6 , pp. 721-729
    • Kurosawa, K.1    Satoh, T.2    Yamamoto, K.3
  • 22
    • 0036649611 scopus 로고    scopus 로고
    • Further constructions of resilient Boolean functions with very high nonlinearity
    • Jul
    • S. Maitra and E. Pasalic, "Further constructions of resilient Boolean functions with very high nonlinearity," IEEE Trans. Inf. Theory, vol. 48, no. 7, pp. 1825-1834, Jul. 2002.
    • (2002) IEEE Trans. Inf. Theory , vol.48 , Issue.7 , pp. 1825-1834
    • Maitra, S.1    Pasalic, E.2
  • 24
    • 35048845264 scopus 로고    scopus 로고
    • Algebraic attacks and decomposition of Boolean functions
    • Advances in Cryptology, EUROCRYPT, Berlin, Germany: Springer-Verlag
    • W. Meier, E. Pasalic, and C. Carlet, "Algebraic attacks and decomposition of Boolean functions," in Advances in Cryptology - EUROCRYPT 2004 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 2004, vol. 3027, pp. 474-491.
    • (2004) Lecture Notes in Computer Science , vol.3027 , pp. 474-491
    • Meier, W.1    Pasalic, E.2    Carlet, C.3
  • 25
    • 0024860262 scopus 로고
    • Fast correlation attacks on certain stream ciphers
    • W. Meier and O. Staffelbach, "Fast correlation attacks on certain stream ciphers," J. Cryptol., vol. 1, pp. 159-176, 1989.
    • (1989) J. Cryptol , vol.1 , pp. 159-176
    • Meier, W.1    Staffelbach, O.2
  • 27
    • 4544247308 scopus 로고    scopus 로고
    • Disjoint linear codes from algebraic function fields
    • Sep
    • H. Niederreiter and C. P. Xing, "Disjoint linear codes from algebraic function fields," IEEE Trans. Inf. Theory, vol. 50, no. 9, pp. 2174-2177, Sep. 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.50 , Issue.9 , pp. 2174-2177
    • Niederreiter, H.1    Xing, C.P.2
  • 28
    • 85027157211 scopus 로고
    • On the construction of highly nonlinear permutations
    • Advances in CryploIogy, EUROCRYPT'92 , Berlin, Germany: Springer-Verlag
    • K. Nyberg, "On the construction of highly nonlinear permutations," in Advances in CryploIogy - EUROCRYPT'92 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 1992, vol. 658, pp. 92-98.
    • (1992) Lecture Notes in Computer Science , vol.658 , pp. 92-98
    • Nyberg, K.1
  • 29
    • 0009995361 scopus 로고    scopus 로고
    • New constructions of resilient and correlation immune Boolean functions achieving upper bounds on nonlinearity
    • Paris, France, Jan
    • E. Pasalic, T. Johansson, S. Maitra, and P. Sarkar, "New constructions of resilient and correlation immune Boolean functions achieving upper bounds on nonlinearity," in Workshop on Coding and Cryptography Proc., Paris, France, Jan. 2001, vol. 6, pp. 425-435.
    • (2001) Workshop on Coding and Cryptography Proc , vol.6 , pp. 425-435
    • Pasalic, E.1    Johansson, T.2    Maitra, S.3    Sarkar, P.4
  • 30
    • 0036672636 scopus 로고    scopus 로고
    • Linear codes in generalized construction of resilient functions with very high nonlinearity
    • Aug
    • E. Pasalic and S. Maitra, "Linear codes in generalized construction of resilient functions with very high nonlinearity," IEEE Trans. Inf. Theory, vol. 48, no. 8, pp. 2182-2191, Aug. 2002.
    • (2002) IEEE Trans. Inf. Theory , vol.48 , Issue.8 , pp. 2182-2191
    • Pasalic, E.1    Maitra, S.2
  • 31
    • 84948968383 scopus 로고    scopus 로고
    • Construction of nonlinear Boolean functions with important cryptographic properties
    • Berlin, Germany: Sprincer-Verlae
    • P. Sarkar and S. Maitra, "Construction of nonlinear Boolean functions with important cryptographic properties," in Advances in Cryptohgy - EUROCRYPT 2000 (Lecture Notes in Computer Science). Berlin, Germany: Sprincer-Verlae, 2000, vol. 1807, pp. 485-506.
    • (2000) Advances in Cryptohgy - EUROCRYPT 2000 (Lecture Notes in Computer Science) , vol.1807 , pp. 485-506
    • Sarkar, P.1    Maitra, S.2
  • 32
    • 84969396978 scopus 로고    scopus 로고
    • Nonlinearity bounds and constructions of resilient Boolean functions
    • Advances in Cryptology, CRYPTO, Berlin, Germany: Springer-Verlas
    • _, "Nonlinearity bounds and constructions of resilient Boolean functions," in Advances in Cryptology - CRYPTO 2000 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlas. 2000, vol. 1880, pp. 515-532.
    • (2000) Lecture Notes in Computer Science , vol.1880 , pp. 515-532
    • Sarkar, P.1    Maitra, S.2
  • 33
    • 85007446434 scopus 로고
    • On constructions and nonlinearity of correlation immune Boolean functions
    • Advances in Cryptology, EUROCRYPT'93 , Berlin, Germany: Springer-Verlae
    • J. Seberry, X. M. Zhang, and Y. Zheng, "On constructions and nonlinearity of correlation immune Boolean functions," in Advances in Cryptology - EUROCRYPT'93 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlae, 1993, vol. 765, pp. 181-199.
    • (1993) Lecture Notes in Computer Science , vol.765 , pp. 181-199
    • Seberry, J.1    Zhang, X.M.2    Zheng, Y.3
  • 34
    • 0021489155 scopus 로고
    • Correlation-immunity of nonlinear combining functions for cryptographic applications
    • Sep
    • T. Siegenthaler, "Correlation-immunity of nonlinear combining functions for cryptographic applications," IEEE Trans. Inf. Theory, vol. IT-30, no. 5, pp. 776-780, Sep. 1984.
    • (1984) IEEE Trans. Inf. Theory , vol.IT-30 , Issue.5 , pp. 776-780
    • Siegenthaler, T.1
  • 35
    • 0021786321 scopus 로고
    • Decrypting a class of stream ciphers using ciphertext only
    • Jan
    • _, "Decrypting a class of stream ciphers using ciphertext only," IEEE Trans. Comp., vol. C-34, no. 1, pp. 81-85, Jan. 1985.
    • (1985) IEEE Trans. Comp , vol.C-34 , Issue.1 , pp. 81-85
    • Siegenthaler, T.1
  • 36
    • 84947755706 scopus 로고    scopus 로고
    • On resilient Boolean functions with maximal possible nonlinearity
    • Proceedings of INDOCRYPT , Berlin, Germany: Springer-Verlag
    • Y. Tarannikov, "On resilient Boolean functions with maximal possible nonlinearity," in Proceedings of INDOCRYPT (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 2000, vol. 1977, pp. 19-30.
    • (2000) Lecture Notes in Computer Science , vol.1977 , pp. 19-30
    • Tarannikov, Y.1
  • 37
    • 0024001951 scopus 로고
    • A spectral characterization of correlation-immune combining functions
    • May
    • G.-Z. Xiao and J. L. Massey, "A spectral characterization of correlation-immune combining functions," IEEE Trans. Inf. Theory, vol. 34, no. 3, pp. 569-571, May 1988.
    • (1988) IEEE Trans. Inf. Theory , vol.34 , Issue.3 , pp. 569-571
    • Xiao, G.-Z.1    Massey, J.L.2
  • 38
    • 0031238366 scopus 로고    scopus 로고
    • Cryptographically resilient functions
    • Sep
    • X. M. Zhang and Y. Zheng, "Cryptographically resilient functions," IEEE Trans. Inf. Theory, vol. 43, no. 5, pp. 1740-1747, Sep. 1997.
    • (1997) IEEE Trans. Inf. Theory , vol.43 , Issue.5 , pp. 1740-1747
    • Zhang, X.M.1    Zheng, Y.2
  • 39
    • 0001136230 scopus 로고    scopus 로고
    • Improving upper bound on nonlinearity of high order correlation immune functions
    • Berlin, Germany: Springer-Verlag
    • Y. Zheng and X. M. Zhang, "Improving upper bound on nonlinearity of high order correlation immune functions," in Selected Areas in Cryptography - SAC '2000 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 2000, vol. 2012, pp. 264-274.
    • (2000) Selected Areas in Cryptography - SAC '2000 (Lecture Notes in Computer Science) , vol.2012 , pp. 264-274
    • Zheng, Y.1    Zhang, X.M.2


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